Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 314

The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.

Effective field theory approach to high-temperature thermodynamics

Open access
Braaten, Eric, Nieto, Agustin·1995·Physical Review D
DOI 10.1103/physrevd.51.6990
Open this paper in CoChat — free account

Abstract

An effective field theory approach is developed for calculating the thermodynamic properties of a field theory at high temperature T and weak coupling g. The effective theory is the three-dimensional field theory obtained by dimensional reduction to the bosonic zero-frequency modes. The parameters of the effective theory can be calculated as a perturbation series in the running coupling constant ${\mathit{g}}^{2}$(T). The free energy is separated into the contributions from the momentum scales T and gT, respectively. The first term can be written as a perturbation series in ${\mathit{g}}^{2}$(T). If all forces are screened at the scale gT, the second term can be calculated as a perturbation series in g(T) beginning at order ${\mathit{g}}^{3}$. The parameters of the effective theory satisfy renormalization group equations that can be used to sum up leading logarithms of T/(gT). We apply this method to a massless scalar field with a ${\mathrm{\ensuremath{\Phi}}}^{4}$ interaction, calculating the free energy to order ${\mathit{g}}^{6}$lng and the screening mass to order ${\mathit{g}}^{5}$lng.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physrevd.51.6990

Cites

16 of 16 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 16 references

Cited by

See all 314

Metadata

Authors
Braaten, E., & Nieto, A.
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1995-06-15
Volume
51
Issue
12
Pages
6990-7006
ISSN
0556-2821 (ISSN-L)
DOI
10.1103/physrevd.51.6990
OpenAlex
W2051170034
Cited by
314
References
16
FWCI
13.80
Type
journal article
Language
en
Open access
green

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Effective field theory approach to high-temperature thermodynamics. https://app.cochat.ai/papers/10.1103/physrevd.51.6990
The paper
Braaten, E., & Nieto, A. (1995). Effective field theory approach to high-temperature thermodynamics. Physical Review D. https://doi.org/10.1103/physrevd.51.6990

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.